Tourists exploring the antique sites of Athens on Monday said they weren't sufficiently worried about Greece's debt crisis to stock up on extra money, despite warnings by some travel groups that bank dispensing machines could shut.

But the bumpy bus rides past near-daily street protests were a reminder that they were visiting a country in trouble.

"You feel the crisis when you're in the bus because you feel all the potholes. Some things are a bit run down," British tourist Marcus Larbalestier said. "Otherwise, so far so good."

Greece is locked in last-ditch talks with its creditors in Brussels for an urgently-needed aid deal to avoid a default that could send it tumbling out of the eurozone.

Failure to agree terms could force Athens to impose capital controls to staunch the recent outflow of billions of euros in recent days, though the Greek government has denied any such plans.

However despite the warnings, tourists' appetite for island holidays in the country appears only slightly dented, with advance demand for package tours still robust.

Just down the steps of the Acropolis hill, which hosts some of Greece's most famous ancient temples, Australian tourist Denise Tilley wasn't worried but instead hoped her visit could make a positive difference.

"We're not concerned. You appreciate you're contributing to the Greek economy," she said.

Tourism accounts for just under a fifth of Greece's economic output and is key to the country's efforts to exit recession after years of painful austerity and unrest.

Just a few steps away at the Acropolis museum of antiquities, a couple visiting from Canada laughed when asked if they had stuffed their hotel deposit box with cash.

"When they heard we were going to Greece, people told us we would get caught up in the crisis but it's all going fine," Colin Cash said, adding he was however a bit worried about possible street protests.

U.S. tourist Seye Ewedemi, visiting from California, said he was also concerned about street protests after his family walked into an anti-austerity rally in front of his hotel on Athens' central Syntagma square on Sunday.

"We got away quickly just in case police charged," he said, while adding that it looked peaceful.

Daniela Dolce, visiting from a country that has made global headlines by defaulting on its debt, brushed aside any worries: "I'm from Argentina, we go through this all the time."

Dimitris Christodoulakis, who works at the front-desk at the Pan Hotel next to Syntagma square, said a number of clients made sure to start the day by taking some cash out of the ATMs - just in case.

"But no one has been calling us up before coming [to Athens] to ask if we have safety deposit boxes," he added.